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arxiv: 2605.23180 · v1 · pith:BJSFZV23new · submitted 2026-05-22 · 💻 cs.CL · cs.LG

Self-Improving In-Context Learning

Baturay Saglam , Dionysis Kalogerias This is my paper

Pith reviewed 2026-05-25 04:53 UTC · model grok-4.3

classification 💻 cs.CL cs.LG
keywords in-context learningprompt optimizationtest-time calibrationself-supervised proxyzeroth-order optimizationfew-shot prompting
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The pith

Optimizing the continuous embeddings of a fixed few-shot prompt at test time improves in-context learning by maximizing a log-probability proxy on the demonstrations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that the log-probabilities a model assigns to the outputs in its own few-shot demonstrations form a usable signal for how well the model has inferred the task. This signal is turned into a bounded self-supervised confidence proxy that can be maximized at test time through zeroth-order optimization of the prompt embeddings. The procedure requires no finetuning, no token generation, no external data, and works for both classification and free-form generation. Experiments across a suite of ICL tasks show the calibrated prompts match or beat the base model and outperform classification-specific baselines on most tasks, with a statistically significant correlation between proxy gains and accuracy gains.

Core claim

The central claim is that the log-probabilities assigned to demonstrated outputs, available from a single forward pass, constitute a reliable optimization signal for in-context learning; maximizing a formal bounded confidence proxy derived from them via zeroth-order search over prompt embeddings yields better task performance on unseen inputs from the same fixed demonstrations.

What carries the argument

A bounded self-supervised confidence proxy derived from the log-probabilities of demonstrated outputs, maximized over continuous prompt embeddings via zeroth-order optimization.

If this is right

  • The calibration procedure matches or improves base-model performance across a range of ICL tasks.
  • It outperforms classification-specific baselines on most evaluated tasks.
  • Statistically significant correlation exists between improvement in the proxy and gains in downstream accuracy.
  • The same procedure applies without modification to both classification and free-form generation tasks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach could be tested on whether the same proxy can guide selection or reweighting of which demonstrations to include in the prompt.
  • It implies that prompt embeddings can be treated as continuous parameters for inference-time adaptation even when the underlying model weights stay frozen.
  • Real-time deployment on streaming inputs might become feasible if the zeroth-order steps can be limited to a small fixed budget per query.

Load-bearing premise

Maximizing the log-probability proxy computed on the fixed demonstrations will produce better predictions on unseen test inputs rather than merely fitting the demonstrations more closely.

What would settle it

If optimizing the proxy produces no corresponding increase (or produces a decrease) in accuracy on held-out test examples, while the base unoptimized prompt remains unchanged, the claim that the proxy encodes a reliable downstream signal would be falsified.

Figures

Figures reproduced from arXiv: 2605.23180 by Baturay Saglam, Dionysis Kalogerias.

Figure 1
Figure 1. Figure 1: Proxy improvement versus accuracy improvement across all 12 ICLEval tasks. A one-sided Spearman rank correlation test (𝐻1 ∶ 𝜌 > 0) yields a statistically significant positive association across all models and tasks combined. (C) (R) (G) Format Check Order Adj. De-duplication Count & Nav. Rel. Analysis Format Conv. Str. Completion List Map. Format Cloning Dup. Check Dict. Search Order Check -0.19 -0.08 -0.0… view at source ↗
Figure 2
Figure 2. Figure 2: Ablation studies of the proposed three-component proxy (𝛼=0.6, 𝛽=0.3, 𝛾=0.1) and the perturbation domain used in end-to-end calibration. (a) Each proxy component is ablated by setting its coefficient to zero and renormalizing the remaining weights. (b) Accuracy difference between the default perturbation domain (demonstration embeddings only) and full-sequence perturbation that includes query positions. Re… view at source ↗
Figure 3
Figure 3. Figure 3: Downstream accuracy under varying perturbation sample counts 𝑁 and perturbation scales, expressed as fractions of the optimal value 𝜇 = 0.004, with all other hyperparameters held fixed. Results are reported for Qwen3-4B, where ( ∗ ) indicates the values used in the main experiments. The confidence component (𝐶̄) is clearly the primary driver of the method’s gains: removing it reduces the fraction of sample… view at source ↗
read the original abstract

We propose to improve in-context learning (ICL) by optimizing the continuous embeddings of a fixed few-shot prompt at test time. The key observation is that the log-probabilities a model assigns to its demonstrated outputs$\unicode{x2013}$available from a single forward pass without generating any tokens$\unicode{x2013}$provide a meaningful signal for how well the model has inferred the task from its demonstrations. We formalize this signal as a bounded, self-supervised confidence proxy and maximize it via zeroth-order optimization over the prompt embeddings, yielding a test-time calibration procedure. The approach requires no finetuning, no token generation, no predefined label set, and no external data, making it equally applicable to both classification and free-form generation tasks. Across a comprehensive suite of ICL tasks, the proposed calibration consistently matches or improves upon the base model and outperforms classification-specific baselines on most tasks. The statistically significant correlation between proxy improvement and downstream accuracy gain confirms that the proposed proxy encodes a reliable optimization signal for in-context learning.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper proposes optimizing the continuous embeddings of a fixed few-shot prompt at test time to maximize a bounded self-supervised confidence proxy based on the model's log-probabilities assigned to the demonstrated outputs (available from a single forward pass). This zeroth-order optimization yields a calibration procedure requiring no finetuning, token generation, predefined label sets, or external data, applicable to both classification and free-form generation. Across ICL tasks the method is reported to match or improve base-model performance, outperform classification-specific baselines on most tasks, and exhibit a statistically significant correlation between proxy improvement and downstream accuracy gains.

Significance. If the central claim holds, the work supplies a lightweight, general test-time adaptation technique for ICL that relies solely on the model's internal signals and extends to generation tasks. The reported correlation supplies empirical grounding for the proxy as an optimization signal. No machine-checked proofs or parameter-free derivations are claimed, but the absence of external data or generation steps is a practical strength.

major comments (2)
  1. [Abstract] Abstract: the claim that the statistically significant correlation 'confirms that the proposed proxy encodes a reliable optimization signal' does not address whether maximizing the demonstration log-prob proxy changes conditional behavior on unseen test inputs or merely increases probability mass on the fixed demonstration tokens; this distinction is load-bearing for the generalization claim.
  2. [Method] Method (zeroth-order optimization description): because the objective is defined exclusively on the fixed demonstrations and never observes test inputs, the manuscript must supply analysis or controls showing that embedding adjustments alter predictions outside the demonstration set rather than overfitting the demonstrated outputs; the current correlation evidence alone leaves this open.
minor comments (1)
  1. Notation for the bounded proxy could be introduced with an explicit equation rather than prose description to improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback, which helps clarify the generalization properties of our test-time optimization procedure. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the statistically significant correlation 'confirms that the proposed proxy encodes a reliable optimization signal' does not address whether maximizing the demonstration log-prob proxy changes conditional behavior on unseen test inputs or merely increases probability mass on the fixed demonstration tokens; this distinction is load-bearing for the generalization claim.

    Authors: We agree the abstract phrasing should be more precise on this point. All downstream accuracy results are measured on held-out test inputs never seen during optimization, and the reported correlation is specifically between proxy gains on the demonstrations and accuracy improvements on those unseen test examples. This already provides evidence that the embedding adjustments affect conditional behavior beyond the fixed demonstrations. We will revise the abstract to explicitly state that the correlation is with test-set accuracy gains, thereby underscoring the generalization aspect. revision: yes

  2. Referee: [Method] Method (zeroth-order optimization description): because the objective is defined exclusively on the fixed demonstrations and never observes test inputs, the manuscript must supply analysis or controls showing that embedding adjustments alter predictions outside the demonstration set rather than overfitting the demonstrated outputs; the current correlation evidence alone leaves this open.

    Authors: We concur that dedicated controls would strengthen the presentation. While the statistically significant correlation with test accuracy (measured on inputs outside the optimization set) already indicates that the adjustments influence predictions on unseen data, we will add a new analysis subsection. This will include quantitative comparisons of model output distributions on test inputs before versus after optimization, along with discussion of the bounded, small-magnitude nature of the zeroth-order updates to address potential overfitting concerns. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained against external test accuracy

full rationale

The central procedure optimizes prompt embeddings to maximize a log-probability proxy computed solely on the fixed demonstration outputs. This proxy is explicitly defined from the model's forward pass on those demonstrations, but the claimed benefit is measured on independent test inputs whose labels are never observed during optimization. The reported statistically significant correlation between proxy improvement and downstream accuracy gain constitutes an external empirical check rather than a definitional reduction. No equations equate the optimized proxy directly to test accuracy by construction, no self-citation chains bear the load, and no uniqueness theorems or ansatzes are smuggled in. The method is therefore not forced to succeed; any observed lift on unseen data stands as a genuine empirical claim.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the domain assumption that the log-prob signal is informative for task inference and on the modeling choice to treat prompt embeddings as continuous optimizable variables; no explicit free parameters or new invented entities beyond the proxy itself are stated.

axioms (1)
  • domain assumption Log-probabilities assigned to demonstrated outputs provide a meaningful signal for how well the model has inferred the task
    Stated as the key observation enabling the proxy; central to the optimization signal.
invented entities (1)
  • bounded self-supervised confidence proxy no independent evidence
    purpose: To serve as an optimizable signal derived from demonstration log-probabilities
    Formalized in the paper from the observed log-prob signal; no independent evidence outside the method itself.

pith-pipeline@v0.9.0 · 5702 in / 1354 out tokens · 40905 ms · 2026-05-25T04:53:48.050943+00:00 · methodology

discussion (0)

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